| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 107 === Manifold learning algorithms are techniques utilized to reduce the dimen sion of data sets. These methods includes the nonlinear (implicit) ones, and the linear (projective) ones. Among the nonlinear are Laplacian eigenmaps and locally linear embeddings (LLE); and among the linear are metric multi dimensional scaling (MDS), ISOMAP, locally preserving projections (LPP) and derivatives of them. All these methods give rise to trace minimization problems and, as a result, eigenvalue problems. We give a common frame work for them and discuss their relationships.
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